Dirichlet spaces and strong Markov processes
نویسندگان
چکیده
منابع مشابه
Dirichlet Forms and Markov Processes
We extend the framework of classical Dirichlet forms to a class of bili-near forms, called generalized Dirichlet forms, which are the sum of a coercive part and a linear unbounded operator as a perturbation. The class of generalized Dirich-let forms, in particular, includes symmetric and coercive Dirichlet forms (cf. Fu2], M/R]) as well as time dependent Dirichlet forms (cf. O1]) as special cas...
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The construction presented in this paper can be briefly described as follows: starting from any “finite-dimensional” Markov transition function pt, on a measurable state space (E,B), we construct a strong Markov process on a certain “intrinsic” state space that is, in fact, a closed subset of a finite dimensional Euclidean space R. Of course we must explain the meaning of finite-dimensionality ...
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We derive sufficient conditions for subgeometric f -ergodicity of strongly Markovian processes. We first propose a criterion based on modulated moment of some delayed return-time to a petite set. We then formulate a criterion for polynomial f -ergodicity in terms of a drift condition on the generator. Applications to specific processes are considered, including Langevin tempered diffusions on R...
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A general technique is given for constructing new Markov processes from existing ones. The new process and its state space are both projective limits of sequences built by an iterative scheme. The space at each stage in the scheme is obtained by taking disjoint copies of the space at the previous stage and quotienting to identify certain distinguished points. Away from the distinguished points,...
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We use Dirichlet form methods to construct and analyse a general class of reversible Markov processes with totally disconnected state spaces. We study in detail the special case of bipartiteMarkov chains. The latter processes have a state space consisting of an \interior" with a countable number of isolated points and a, typically uncountable, \boundary". The equilibrium measure assigns all of ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1971
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1971-0295435-0